Mufflers with catalytic converters for combustion engines are well-known since a very long time, especially for cars. For portable power equipment, such as chain saws, they have been available on the market to a small extent since the end of the 1980's. Demands for low weight, size and cost have contributed towards the fact that catalytic converter technology was put into practice considerably later within this field. The catalytic mufflers, which have been used for portable equipment, have as a rule consisted of a converter element comprising coated, thin sheet metal strips. A pleated or corrugated metal strip can for instance be rolled together with a plane strip into a cylindrical element. Both strips are coated with a catalyzing layer, and the exhaust emissions are conducted through the axial cavities, which are formed between the strips, and are hereby cleaned. The catalytic converter element is relatively sensitive to vibrations and demands an elaborately designed mounting in order to get an acceptable length of life, seen from a purely mechanical point of view. The mounting itself demands additional details in the muffler, for instance a sleeve, which shall serve as an enclosure of the element. Furthermore, the muffler must be designed so that the catalytic converter element functions as a passage in the muffler, for instance located in an exhaust pipe out of the muffler. This implies certain restrictions for the muffler, since it is hardly reasonable from a cost point of view to use several smaller catalytic elements, which serve as parallel passages in the muffler. Thus, the usage of a converter element implies certain restrictions when designing the muffler, and this could bring about a reduced silencing effect. Both the converter element itself and its mounting are relatively costly, and this brings about a considerably more expensive muffler in total. When the converter element is used in a muffler for two-stroke engines, problems can also arise with a very high temperature in the converter element. This is due to the fact that the exhaust gases from the two-stroke engine contain a high content of unburned hydrocarbons, which are burned in the converter element. This partly leads to a very high heat generation in the converter element and partly to very hot exhaust gases. The converter element often reaches temperatures exceeding 1000 degrees C and must therefore be cooled down, for instance by means of heat dissipation. This must take place without the muffler's casing overheating anywhere, considering user-safety and legal requirements. The local heat generation in the converter element is consequently a problem.